Three Further Constraints - On Learning Conditional Information

Appendix 3: On Learning Conditional Information

4.2 Three Further Constraints

In addition to the cases we have already considered, MacFarlane (manuscript: pp. 11-2) uses the following constraints to adjudicate between possible bridge principles. Since his concern is with the relationship between logical consequence and rational beliefs, we will need to consider whether something equivalent holds for the case of public commitments.

The first is the strictness test, which holds that for the general case, the agent has not done everything that he ought to, if he only believes p but not its logical consequence, q.

Although our first bridge principle did not capture the exact wording of this constraint, a case could be made that it managed to capture the gist of it by requiring that the speaker accepts challenges based on the logical consequences of his acknowledged commitments. At this point it is unclear whether anything further is needed or whether this conditional task responsibility already succeeds in making the relation between p and its logical consequences sufficiently strict.

The second is whether the proposed bridge principle is capable of getting the priority right so that we can still say that:

We seek logical knowledge so that we will know how we ought to revise our beliefs: not just how we will be obligated to revise them when we acquire this logical knowledge, but how we are obligated to revise them even now, in our state of ignorance. (ibid.)

This concern arises, because if we were only normatively constrained by known logical consequences, it seems that “[t]he more ignorant we are of what follows from what, the freer we are to believe whatever we please” (ibid.), which seems to get things backwards.

More specifically, the concern in our context might be that since the speaker only has to acknowledge the logical consequence of his acknowledged commitments as consequential commitments by accepting suitable challenges, the speaker gets off the hook more easily the more ignorant his scorekeepers are. In response, it can be pointed out that the speaker’s responsibility to accept such challenges does not come with an expiration date.¹⁰⁷ So he will continue to be liable to criticism, if his assertions are shown to be logically incoherent as our knowledge about the logical consequences grows. (Or rather, the

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expiration date is the point, where we can no longer consider the agent’s assertions as uncontroversial starting points for further inquiry, because our knowledge has grown too much in the intermediary time. But this does not guard the original agent from revision through ignorance, because what it means is merely that the assertions will lose their epistemic significance once the ignorance is overcome, if there was anything problematic about them in the first place.)

Moreover, it will still be possible to maintain on the basis of the present approach that we seek logical knowledge so as to prevent error from propagating. Hence, there will still be a pressure towards overcoming our state of ignorance on the present proposal.

Similarly it holds for the scorekeeper that—although he is only permitted and not required to add the logical consequences as consequential commitments to the speaker’s score according to bridge principle (II)—he risks contributing to the propagation of error, whenever he refrains from exercising this right. So he too is under pressure to overcome a state of ignorance.

The final constraint consists in being able to maintain that an agent, who refuses to take a stand on a logical consequence (e.g. their conjunction) of his beliefs is acting in a way that he ought not to. As we have seen, bridge principle (I) postpones the need for the speaker to take a stand on the logical consequences of his acknowledged commitments until a suitable challenge emerges, and it is this feature of the present account that ensures that excessive demands are not imposed on the speaker. But on the other hand, it is not clear why the agent should be forced to take a stance on all the logical consequences of his acknowledged commitments in the absence of a well-grounded suspicion about unmet, severe challenges. It might be prudent for the speaker to consider some of the most obvious logical consequences of his assertions before making them to avoid having to withdraw them immediately in the face of embarrassing challenges. But it is not obvious why it would constitute a failure of his epistemic responsibility as long as he is prepared to withdraw them if severe challenges emerge. And, of course, at that point (I) no longer licenses him to refrain from taking a stance on the logical consequences of his acknowledged commitments.

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According to bridge principle (II), the scorekeeper is not required to take a stance on all the logical consequences of the speaker’s acknowledged commitments. And it is this feature of the present account that ensures that excessive demands are not imposed on the scorekeeper. But here too it is unclear why it should be problematic that the scorekeeper refuses to take a stance on whether a logical consequence could be added to the speaker’s score as a consequential commitment, unless there was some well-grounded suspicion that the scorekeeper might thereby contribute to avoiding the propagation of error. So here too our bridge principles don’t seem to collide with MacFarlane’s (manuscript) criteria of adequacy.

5. Conclusions and Future Work

It then appears that the present account is capable of handling the problematic cases that Harman (1986) discusses as well as the further constraints that MacFarlane (manuscript) considers. The significance of this contribution consists in that MacFarlane presents these various desiderata as standing in a tension and thus requiring some sort of trade-off, which has been avoided on the present account.

By theorizing about public commitments instead of beliefs, we are able to treat cases of inconsistency as harmless cases of incompatible obligations that cannot all be redeemed at once. By invoking the distinction between doxastic perspectives, and making it the task of the scorekeeper to construct a deontic score for the speaker that meets the minimal requirements of belief sets to decide whether entitlement can be attributed, we are able to drive a wedge between assessments of the speaker’s rationality and assessments of which information we want to use for further inquiry.

This move allows the speaker to be rationally permitted to maintain inconsistent doxastic commitments, when confronted with conflicting requirements while allowing his scorekeepers to take measures to prevent errors from propagating. Moreover, we have seen that it comes with the further nicety that we can continue to remain uncommitted about revisionism about logic while avoid letting ex falso quodlibet ruin the deontic score of the

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speaker by adding commitment to random propositions, whenever the speaker finds himself in situations of this kind.

An area for further investigation is a general comparison between the respective advantages and disadvantages of formulating the bridge principles in terms of public commitment or rational beliefs. It is surely of central importance when dealing with this issue that while it is not completely voluntarily what we believe (in the sense that if we really believe something, we cannot just decide to stop believing in it whenever we want (ibid: 15)), our acknowledged commitments is something that we can exercise full control over. For this reason it might be more natural to think about potentially conflicting obligations in terms of public commitments than in terms of beliefs, which would thereby restrict a central tool for dealing with inconsistencies to bridge principles formulated in terms of public commitments.¹⁰⁸

The upshot of this final chapter has been that one can make the normative foundation of ranking theory more palatable by viewing it as applying to public commitments attributed in argumentative contexts instead of to beliefs in individual reasoning. As such, this approach to the problem of logical omniscience opens up for a new avenue of research in psychology. The take home message has been that if we are interested in the extent to which consistency, deductive closure, and the equivalent treatment of logically equivalent propositions provide a suitable normative foundation, we should not look at whether the participants actually succeed in complying to these norms in their own individual reasoning, but rather at the extent to which they recognize being bound by them in argumentative contexts through the justificatory challenges they pose and accept.

More generally, this reorientation connects with the work of Mercier & Sperber (2011), who have recently made an influential case that the primary function for which reasoning evolved is the production and evaluation of arguments. In support of this claim they cite a range of circumstantial evidence. Probably the most convincing of which is the finding that once the Wason selection task¹⁰⁹ was posed in groups, where the participants could deliberate about the solution in an argumentative context, the performance went up from the usual ca. 10 %¹¹⁰ to about 70 % (and even to 80 %, when they had first been

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presented with the problems on an individual basis). Moreover, this drastic improvement in performance was not merely the result of there being one individual in each group, who had come up with the correct solution and shared it with the others, as the verbal transcripts clearly show how some groups were able to jointly assemble all the pieces of the puzzle (Moshman & Geil, 1998).

Of course, such findings do not conclusively settle the issue about the evolutionary function of reasoning. But they do make it interesting to follow the approach sketched in this chapter to test whether the norms are being recognized in an argumentative setting as opposed to in individual reasoning.

From a philosophical perspective, one of the interesting corollaries of this reorientation is that it opens up for the application of the axioms of belief revision theory embodied in ranking theory to yield a formal account of the score of consequential commitments that the scorekeeper keeps on the speaker. In this context, it is interesting to observe that ranking theory was in part developed to solve the problem of iterated belief change in belief revision theory (Spohn 2012: ch. 4- ) and that Schaefer’s ( 01 ) whole dissertation is devoted to the problem of how to modify Brandom’s account of defeasible reasoning to allow for the recovery of entitlement that has been defeated through the addition of further commitments. So here the former has the prospect of enriching the latter approach.

Second, the conditionalization rule in ranking theory could be applied to give us a precise account of the updating of entitlement of a deontic score. These observations all open up for new avenues of promising research.

Finally, through its explication of the reason relation, ranking theory provides a natural formal framework for making the inferential relations that Brandom uses to explicate propositional content precise, as we have seen. Based on this explication, Brandom can be viewed as advancing a global ranking-theoretic (or probabilistic) reason relation semantics. Within the present dissertation, this semantic analysis has been applied to the conditional connective. However, instead of following Brandom in proposing a general alternative to truth-conditional semantics, chapter II contained the compromise that we should integrate reason relations in the sense dimension of meaning and view both

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the decoding of truth conditions and argumentative structure as core components of linguistic competence.

91 Acknowledgement: this chapter profited from discussions with Wolfgang Spohn, Michael De, Lars Dänzer, Eric Raidl, and the other members of a reading group on The Laws of Belief at the University of Konstanz. I would also like to thank the participants at Thomas Müller’s colloquium, Keith Stenning, and the audience at AISB50 for discussion.

92 Predecessors: in a way Levi (1991: ch. 2, 1997: ch. 1) was the first to emphasize that one could make progress with respect to the problem of logical omniscience by thinking of it in terms of commitments rather than in terms of belief. Subsequently, Milne (2009) has gone down a similar route. What the present treatment adds is giving it a more Brandomian spin (which was already implicit in Milne (2009)) and by formulating bridge principles that are capable of dealing with the constraints presented in MacFarlane (manuscript).

93 Explication of the framing effect: it has been shown that different ways of presenting the same information will give rise to different emotions, which in turn affects our judgments and decision making. Accordingly, the statement ‘the odds of survival one month after surgery are 90 %’ will be found more reassuring than the equivalent statement ‘mortality within one month of surgery is 10 %’

(Kahneman, 2012: 88). As a result, participants will respond differently to these two statements in spite of their logical equivalence.

94 On Brandom’s notion of material inferences: it should be noted that material inferences are used as a generic notion for content based inferences in the writings of Brandom. To be sure, Brandom does not accept the analytic/synthetic distinction for familiar Quinean reasons, but his notion of material inferences covers both what would otherwise be thought of as following in both of these categories. In his writings one thus not only finds examples of material inferences that sound like analytical inferences, like the example in the text, but also examples like inferring that a banana is ripe from its being yellow (Brandom, 2010: 104).

95 Qualification concerning a weaker notion: this is, of course, the strictest explication possible of the notion of commitment preservation. In principle, one could also just demand that (q|Γ) = c for some high number, c. However, the version in the text was chosen, because Brandom says that the notion of commitment preservation generalizes the category of deductive inferences.

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96 Refinement through J-conditionalization: to allow for cases where P(Γ) < 1, the third condition could be replaced by Jeffrey conditionalization as follows: > b, for

> 0.

97 Inferentialism as a probabilistic reason relation semantics: by exploiting the idea from Spohn (2012:

ch. 6) that p is a reason for q whenever (q|p) > (q|¬p), and that p is a reason against q whenever (q|p)

< (q|¬p), the weak and the strong notions of incompatibility are treated as cases of when p is an inductive or a deductive reason against q, and entitlement preservation and commitment preservation are treated as cases, where the set Γ counts as an inductive or a deductive reason for q. This explication treats inferentialism as a rank-theoretic (or probabilistic) reason-relations semantics, and it is in general agreement with Dorn’s ( 00 ) account of the strength of arguments. However, this explication can only be partial, because it needs to be supplemented with Brandom’s pragmatic account of the conditions under which the scorekeeper should add and subtract commitments and entitlements from the speaker’s score, which Kibble (2005, 2006a, 2006b) has begun to formalize.

98 Clarification on assertion: actually on Brandom’s view making an assertion is putting forward a claim as something that the hearer can use as a premise in his/her own reasoning and not: putting it forward as an uncontroversial starting point for further inquiry. The reason why the argument was nevertheless formulated in the latter way was to bracket the issue of reductios. The point is that while reductios use the speaker’s assertions as premises in one’s own reasoning, the premises in reductios cannot be thought of as uncontroversial starting points for further inquiry. Rather I take it that reductios can be seen as a dialectical tool that scorekeepers use to show that there is a problem with the speaker’s constellation of commitments. (I thank Michael De for forcing me to clarify this point.)

99 On the use of conditionals in the bridge principles: MacFarlane (manuscript) says that the conditional can be read as the material implication in the formulation of these principles (at least to begin with). But I am not sure whether this is a good idea in light of the paradoxes of the material implication according to which ¬p p q for any arbitrary q, as it could introduce bridge principles of any arbitrary degree of absurdity for when C is not a logical consequence of A and B. Alternatively a semantics for the conditional could be preferred, where the paradoxes of the material implication are avoided.

100 Reference: http://podcasts.ox.ac.uk/people/hartry-field.

101 Separating a weak and a strong version: notice that it would also be possible to hold the view that the deontic score built up in the course of a conversation would be ruined completely by an inconsistency.

Instead, a weaker version was put forward here, according to which entitlement is only withheld with respect to the assertions producing the inconsistency (e.g. p and q, where q entails non-p) and not with

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respect to the whole deontic score. Yet, repeated instances of such failures can diminish one’s trust in the agent, which is why the idea of blacklisting recurrent sinners is introduced below.

102 Explication of the liar paradox: one version of the liar paradox runs as follows. The second sentence in this endnote is not true. Suppose the second sentence is true, then it is true that the second sentence is not true, and so the second sentence must not be true. Suppose it is not true, then things are as the second sentence says they are, and so it must be true.

103 Reference: personal communication.

104 Parallel to Moore’s paradox: in exhibiting this difficulty in asserting something about one’s own doxastic perspective that one would be able to assert about a foreign doxastic perspective, the preface paradox bears some similarity to Moore’s paradox, which consists in that we cannot assert sentences such as ‘p, but I do not believe that p’ or ‘p, but I believe that non-p’ without it sounding paradoxical—in spite of the fact that it is perfectly possible for any agent that p is the case and that this agent either believes that non-p or fails to believe that p (cf. Brandom 1994: 605). In both cases we seem to be faced with things that we know hold with respect to any other doxastic perspective (and a fortiori to our own), but that we cannot assert directly about our own doxastic perspective. Perhaps the best that the author can do is to restrict himself to counterfactuals about how he would have acted as a scorekeeper if the book had been written by somebody else.

105 Caveat concerning the reason relation explications: the explication in section 2.1 did not quite capture this feature of Brandom’s account by adding the requirement that P(Γ) > a on entitlement preservation, which found no parallel in the explication of commitment preservation. So this is one of the senses in which it was only offered as a first approximation. Another related sense in which it is only offered as a first approximation is that it does not yet contain a formal representation of a commitment to p. Yet, one might argue that just as a formal representation of entitlement had to be part of the explication of entitlement preservation, so a formal representation of commitment has to be part of the explication of commitment preservation.

106 Acknowledgement: I thank Michael De for helping me to clarify this point.

107 On commitments without an expiration date: as the practice of defending the works of deceased philosophers shows, the deontic score of an agent can outlive his biological time in virtue of other agents stepping in and administering the commitments of a deceased agent either as he would have been disposed to or in the way that would have been most optimal.

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